Numerical models of thermally activated convective flow in Earth's mantle do not resemble active plate tectonics because of their inability to model successfully the process of subduction, other than by the inclusion of artificial weak zones. Here we show, using a boundary layer argument, how the ''rigid lid'' style of convection favored by thermoviscous fluids leads to lithospheric stresses which may realistically exceed the yield stress and thus cause subduction to occur through the visoc-plastic failure of lithospheric rock. An explicit criterion for the failure of the lid is given, which is sensitive to the internal viscosity &eegr;a below the lid. For numbers appropriate to Earth's mantle, this criterion is approximately &eegr;a>1021 Pa s. ¿ American Geophysical Union 1993